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2 years ago

Point B is in the interior of ∠AOC, m∠AOC = 108°, m∠AOB = 3m∠BOC. Find m∠AOB.

2 answers:

6 0

If point is the interior of <AOC ,
then m<AOB + m<BOC = m< AOC ( angle addition postulate ) eq 1
(3m<BOC ) + m <BOC = m <AOC { m<AOB = 3m<BOC)
4m <BOC = 108
m<BOC = 27

m<AOB + m <BOC = m < AOC
m<AOB = 108 - 27
m <AOB = 81

Anna007 [38]2 years ago

5 0

Answer:

The measure of point B is 36 degrees

Step-by-step explanation:

Since point B is in the interior of the angle AOC, we take the measure of AOC and divide it by 3. You should get 36.

Formula: 3x=108

x=36

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Peter mixes 4 1/2 cups of orange juice, 2 1/4 of ginger ale and 6 1/3 cups of strawberry lemonade to make some punch. What is th

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To add these amounts together, we must first find their least common multiple in order to get common denominators (b/c when you add fractions, the denominators must be the same).

We'll start by listing some of their multiples.
To do this, count by whatever the denominator is:
4 1/2 (denominator is 2): 2 4 6 8 10 12 14
2 1/4 (denominator is 4): 4 8 12 16
6 1/3 (denominator is 3): 3 6 9 12 15

Look and see which is the first multiple that all three denominators have. Circle them if it helps you. In this case, it's 12.

So now we have to multiply the denominators by whatever number it takes to reach 12, and multiply by the same number to the numerator:

4 1/2 (times 6 to both top and bottom) =
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2 1/4 (times 3) = 2 3/12

6 1/3 (times 4) = 6 4/12

Add all these fractions together, and you get 12 13/12, which is equal to 13 1/12.

Thus, Peter makes a total of 13 1/2 cups.

Hope this made sense! tell me if anything is confusing/incorrect :))

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2 years ago

Derive an equation d = acos(bt) for the displacement d (in feet) in relation to sea level of a piece of cloth tied to a water wh

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2 years ago

Jennet graphs the inequality Negative 6 less-than x on the number line below.

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Answer:

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Step-by-step explanation:

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2 years ago

The HCF of the greatest 2- digit number and the greatest 3-digit number is

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Answer:

Step-by-step explanation:

So the greatest 2 digit number is 99 and the greatest 3 digit number is 999

So find the hcf ( highest common factor ) of 99 and 999.

Factors of 99 : 1, 3, 9, 11, 33, 99

Factors of 999 : 1, 3, 9, 27, 37, 111, 333, 999

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HOPE IT HELPED

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2 years ago

If quadrilateral PQRS is a rectangle, then which of the following is true?

brilliants [131]

∠STP ≅ ∠QTR is the True statement ⇒ answer C

Step-by-step explanation:

In any rectangle

1. Each two opposite sides are equal and parallel

2. The measure of its vertex angles is 90°

3. The two diagonals are equal

Now lets find the true statements

∵ PQRS is a rectangle

∴ PS = QR ⇒ opposite sides

∴ PQ = SR ⇒ opposite sides

∴ PR = QS ⇒ diagonals

A. ∠PSQ ≅ ∠QSR

∵ The diagonals of the rectangle do not bisect the vertex angles

∴ AQ does not bisect angle S

∴ m∠PSQ ≠ m∠QSR

∴ ∠PSQ not congruent ∠QSR

∠PSQ ≅ ∠QSR ⇒ False

B. segment SR ≅ segment RQ

∵ SR and RQ are two adjacent sides

∵ The adjacent side in the rectangle not equal

∴ SR ≠ QR

∴ segment SR not congruent to segment RQ

segment SR ≅ segment RQ ⇒ False

C. ∠STP ≅ ∠QTR

∵ PR intersects QS at point T

∴ m∠STP = m∠QTR ⇒ vertically opposite angles

∴ ∠STP ≅ ∠QTR

∠STP ≅ ∠QTR ⇒ True

D. segment PS ≅ segment PR

∵ PS is a side in the rectangle

∵ PR is a diagonal in the rectangle

∵ The side of the rectangle not equal the diagonal of the rectangle

∴ PS ≠ PR

∴ segment PS not congruent to segment PR

segment PS ≅ segment PR ⇒ False

∠STP ≅ ∠QTR is the True statement

Learn more:

You can learn more about rectangle in brainly.com/question/6594923

#LearnwithBrainly

8 0

2 years ago

Read 2 more answers